Related papers: Unified computational approach to nilpotent algebr…

Let $\mathcal{B}_\mathfrak{q}$ be a finite-dimensional Nichols algebra of diagonal type corresponding to a matrix $\mathfrak{q}$. We consider the graded dual $\mathcal{L}_{\mathfrak{q}}$ of the distinguished pre-Nichols algebra…

We develop methods for computing with matrix groups defined over a range of infinite domains, and apply those methods to the design of algorithms for nilpotent groups. In particular, we provide a practical algorithm to test nilpotency of…

In this paper, a nilpotency criterion is given for finite dimensional alternative superalgebras in the spirit of Engel's Theorem for Jordan superalgebras over infinite fields provided by Shestakov and Okunev. For alternative superalgebras,…

We give a full classification of 6-dimensional nilpotent Lie algebras over an arbitrary field, including fields that are not algebraically closed and fields of characteristic~2. To achieve the classification we use the action of the…

Every non-solvable and non-semisimple quadratic Lie algebra can be obtained as a double extension of a solvable quadratic Lie algebra. Thanks to a partial classification of nilpotent Lie algebras and this result, we can design different…

We prove the solvability and nilpotency of Kac--Paljutkin's finite quantum group and Sekine quantum groups and we classify the solvable series of Kac--Paljutkin's finite quantum group via Cohen--Westreich's Burnside theorem. Some semisimple…

We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…

This paper deals with the variety of commutative nonassociative algebras satisfying the identity $L_x^3+ \gamma L_{x^3} = 0$, $\gamma \in K$. Correa et al proved that if $\gamma = 0,1$ then any such finitely generated algebra is nilpotent.…

We investigate the filtration corresponding to the degree function induced by a non-zero locally nilpotent derivations and its associated graded algebra. As an application we provide an efficient method to recover the Makar-Limanov…

We show that for every complex simple Lie algebra, the equations of Schubert divisors on the flag variety give a complete integrable system of the minimal nilpotent orbit. The approach is motivated by the integrable system on Coulomb…

The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. The motivation to write this paper is an unpublished yet result of J.R.Gomez, B.A.Omirov on necessary and sufficient conditions…

We give a classification of $5$- and $6$-dimensional complex one-generated nilpotent bicommutative algebras.

Classification of finite dimensional representations of the q-deformed Heisenberg algebra $H_q(3)$ is made by the help of Clifford algebra of polynomials and generalized Grassmann algebra. Special attention is paid when $q$ is a primitive…

Randomized methods, such as the randomized SVD (singular value decomposition) and Nystr\"om approximation, are an effective way to compute low-rank approximations of large matrices. Motivated by applications to operator learning, Boull\'e…

CLIFFORD performs various computations in Grassmann and Clifford algebras. It can compute with quaternions, octonions, and matrices with entries in Cl(B) - the Clifford algebra of a vector space V endowed with an arbitrary bilinear form B.…

We have recently shown that pseudo-bosonic operators realize concrete examples of finite dimensional nilpotent Lie algebras over the complex field. It has been the first time that such operators were analyzed in terms of nilpotent Lie…

The condition of nilpotency is studied in the general linear Lie algebra $\mathfrak{gl}_{n}(\mathbb{K})$ and the symplectic Lie algebra $\mathfrak{sp}_{2m}(\mathbb{K})$ over an algebraically closed field of characteristic 0. In particular,…

We explicitly construct, in terms of Gelfand--Tsetlin tableaux, a new family of simple positive energy representations for the simple affine vertex algebra V_k(sl_{n+1}) in the minimal nilpotent orbit of sl_{n+1}. These representations are…

A compatible nilpotent Leibniz algebra is a vector space equipped with two multiplication structures that interact in a certain natural way. This article presents the classification of these algebras with dimensions less than four, as well…

We present algorithms to compute generalized root systems of Nichols algebras of diagonal type and of contragredient Lie superalgebras. As a consequence, we obtain an algorithm to compute the Lyndon words in the Kharchenko PBW basis…